I would choose the exponential form which makes it a matter of algebraic manipulation, but using trigonometric identities is equality valid.
[tex]sin(\theta) = \frac{e^{i\theta} - e^{-i\theta}}{2i}[/tex]
and [tex]cos(\theta) = = \frac{e^{i\theta} + e^{-i\theta}}{2}[/tex]
substituting in the original equation, you'll eventually end up with an expression of the form
[tex]\frac{e^{ix} - e^{-ix} + e^{iy} - e^{-iy}}{4i}[/tex]
getting that back to the trigonometric form, you should end up with two easy integrals, namely the integral of 1/2sin(x) + 1/2sin(y)